There is a very large market fo plastic bags having zipper closures, and the market extends from the every inexpensive light gauge bags up to the high quality heavy gauge bags. There are two forms of bags having zippers. One form of bag with zipper is made by extruding the zipper and the bag simultaneously so there is no problem in providing the bags in any desired thickness. Another form of bag with zipper is made by applying a strip of zipper material to plastic sheet material during the formation of plastic bags. In this latter form of zipper bag, there have been limits in the weight of bag material that can be used because of the relatively heavy gauge in which the zipper material is provided. The zipper material is customarily around 8 mils or so, while there is a large market for plastic bags having a thickness of around 1 mil. Due to the vast difference in thickness, if the materials are heated sufficiently to melt the heavy material enough to effect a weld, the thin material is melted to the point that it loses its integrity and no weld can be made. Conversely, if the materials are heated only sufficiently to melt the thin material enough to allow a weld, the thick material is not hot enough and no weld can be made.